D) Some powers of the matrix
Matrix^2
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 5 2 1 2 1 . 2 . 1 1 1 1 . 2 4 2 2 1 1 2 . 1 . 2 2 . 2 2 2 3
[2,] 2 6 1 1 2 1 3 3 3 1 2 2 1 . 3 2 1 2 1 . 2 2 2 2 1 2 4 . 3 .
[3,] 1 1 5 . . . 4 1 2 1 1 . . 1 4 2 1 1 . . 3 2 . 2 . 2 1 1 . 1
[4,] 2 1 . 6 2 1 1 2 3 . 1 4 . 3 1 1 2 . . 2 1 3 1 3 1 2 4 3 2 3
[5,] 1 2 . 2 7 2 2 2 3 2 1 1 . 2 3 2 2 1 1 . 2 2 2 2 . 2 2 . 4 3
[6,] . 1 . 1 2 6 2 3 2 3 2 . . 2 2 1 2 1 3 2 3 1 3 2 1 2 1 . 3 .
[7,] 2 3 4 1 2 2 10 2 2 1 3 1 . 2 5 4 4 1 . 2 3 2 . 4 2 3 3 1 1 3
[8,] . 3 1 2 2 3 2 6 3 1 1 2 1 2 2 1 2 2 2 . 3 2 3 2 . 4 3 . 2 .
[9,] 1 3 2 3 3 2 2 3 10 3 2 3 1 1 2 2 3 3 2 1 2 5 4 4 1 4 2 1 4 .
[10,] 1 1 1 . 2 3 1 1 3 9 2 . . 1 4 2 2 3 2 1 5 1 4 3 . 4 . . 3 .
[11,] 1 2 1 1 1 2 3 1 2 2 6 . . . 3 1 1 1 1 1 4 1 2 2 2 3 2 . 2 .
[12,] 1 2 . 4 1 . 1 2 3 . . 7 1 2 1 1 2 1 . 2 . 5 3 4 2 1 3 2 1 3
[13,] . 1 . . . . . 1 1 . . 1 1 . . . . 1 . . . 1 1 1 . . . . 1 .
[14,] 2 . 1 3 2 2 2 2 1 1 . 2 . 7 2 3 4 . 1 2 . 2 1 4 . 1 3 3 2 4
[15,] 4 3 4 1 3 2 5 2 2 4 3 1 . 2 11 3 2 2 2 1 5 3 1 6 2 3 2 1 2 3
[16,] 2 2 2 1 2 1 4 1 2 2 1 1 . 3 3 9 3 2 . 1 1 . . 4 1 3 2 2 2 3
[17,] 2 1 1 2 2 2 4 2 3 2 1 2 . 4 2 3 9 . 1 3 . 2 2 4 2 2 3 1 1 3
[18,] 1 2 1 . 1 1 1 2 3 3 1 1 1 . 2 2 . 6 2 . 2 1 2 1 . 4 . . 3 .
[19,] 1 1 . . 1 3 . 2 2 2 1 . . 1 2 . 1 2 4 1 1 1 2 1 1 1 . . 2 .
[20,] 2 . . 2 . 2 2 . 1 1 1 2 . 2 1 1 3 . 1 5 . 2 1 2 3 . 1 1 2 3
[21,] . 2 3 1 2 3 3 3 2 5 4 . . . 5 1 . 2 1 . 8 1 3 2 . 5 2 . 2 .
[22,] 1 2 2 3 2 1 2 2 5 1 1 5 1 2 3 . 2 1 1 2 1 9 4 6 2 1 3 1 2 3
[23,] . 2 . 1 2 3 . 3 4 4 2 3 1 1 1 . 2 2 2 1 3 4 8 1 1 3 2 . 3 .
[24,] 2 2 2 3 2 2 4 2 4 3 2 4 1 4 6 4 4 1 1 2 2 6 1 12 2 1 2 2 2 4
[25,] 2 1 . 1 . 1 2 . 1 . 2 2 . . 2 1 2 . 1 3 . 2 1 2 4 . 1 . 1 2
[26,] . 2 2 2 2 2 3 4 4 4 3 1 . 1 3 3 2 4 1 . 5 1 3 1 . 9 3 . 2 .
[27,] 2 4 1 4 2 1 3 3 2 . 2 3 . 3 2 2 3 . . 1 2 3 2 2 1 3 7 2 2 2
[28,] 2 . 1 3 . . 1 . 1 . . 2 . 3 1 2 1 . . 1 . 1 . 2 . . 2 4 1 3
[29,] 2 3 . 2 4 3 1 2 4 3 2 1 1 2 2 2 1 3 2 2 2 2 3 2 1 2 2 1 8 2
[30,] 3 . 1 3 3 . 3 . . . . 3 . 4 3 3 3 . . 3 . 3 . 4 2 . 2 3 2 8
Matrix^5
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 414 670 438 590 697 682 811 759 1099 898 617 602 129 591
[2,] 670 824 662 846 831 703 1250 834 1271 843 701 896 154 900
[3,] 438 662 364 679 615 510 731 675 964 570 492 756 144 600
[4,] 590 846 679 672 847 823 1180 882 1204 1142 862 643 128 714
[5,] 697 831 615 847 904 853 1218 915 1233 973 738 836 143 983
[6,] 682 703 510 823 853 646 1066 708 1041 752 570 797 123 951
[7,] 811 1250 731 1180 1218 1066 1392 1306 1927 1282 976 1300 285 1099
[8,] 759 834 675 882 915 708 1306 808 1187 853 714 906 141 970
[9,] 1099 1271 964 1204 1233 1041 1927 1187 1670 1240 1114 1190 184 1321
[10,] 898 843 570 1142 973 752 1282 853 1240 776 670 1089 139 1236
[11,] 617 701 492 862 738 570 976 714 1114 670 542 893 144 867
[12,] 602 896 756 643 836 797 1300 906 1190 1089 893 598 121 680
[13,] 129 154 144 128 143 123 285 141 184 139 144 121 16 153
[14,] 591 900 600 714 983 951 1099 970 1321 1236 867 680 153 754
[15,] 987 1379 848 1513 1451 1226 1710 1522 2144 1384 1100 1550 275 1469
[16,] 674 959 557 914 985 976 1135 1018 1523 1115 872 959 199 877
[17,] 795 1112 714 898 1146 1014 1321 1106 1610 1328 957 885 200 924
[18,] 603 568 431 725 615 498 976 552 828 509 482 755 94 791
[19,] 435 425 323 507 531 385 708 426 619 442 345 484 62 606
[20,] 404 615 419 473 640 598 757 650 914 839 564 444 106 512
[21,] 849 862 606 1202 953 698 1264 889 1323 734 646 1241 174 1229
[22,] 848 1232 956 990 1150 1021 1735 1241 1591 1294 1097 938 173 1045
[23,] 865 816 745 900 883 672 1431 764 1081 821 704 848 104 1082
[24,] 1019 1592 1020 1394 1583 1435 1980 1675 2240 1692 1405 1321 264 1344
[25,] 333 534 372 434 523 467 661 566 821 639 460 429 98 435
[26,] 981 968 713 1207 1033 806 1460 929 1440 913 798 1274 184 1242
[27,] 721 981 791 870 990 897 1353 1007 1492 1219 908 905 179 903
[28,] 259 477 327 334 474 517 561 526 711 717 513 325 80 321
[29,] 827 899 716 960 1001 924 1469 948 1347 1092 829 936 141 1154
[30,] 477 906 582 658 909 983 1021 1058 1372 1281 878 642 166 659
[1,] 987 674 795 603 435 404 849 848 865 1019 333 981 721 259
[2,] 1379 959 1112 568 425 615 862 1232 816 1592 534 968 981 477
[3,] 848 557 714 431 323 419 606 956 745 1020 372 713 791 327
[4,] 1513 914 898 725 507 473 1202 990 900 1394 434 1207 870 334
[5,] 1451 985 1146 615 531 640 953 1150 883 1583 523 1033 990 474
[6,] 1226 976 1014 498 385 598 698 1021 672 1435 467 806 897 517
[7,] 1710 1135 1321 976 708 757 1264 1735 1431 1980 661 1460 1353 561
[8,] 1522 1018 1106 552 426 650 889 1241 764 1675 566 929 1007 526
[9,] 2144 1523 1610 828 619 914 1323 1591 1081 2240 821 1440 1492 711
[10,] 1384 1115 1328 509 442 839 734 1294 821 1692 639 913 1219 717
[11,] 1100 872 957 482 345 564 646 1097 704 1405 460 798 908 513
[12,] 1550 959 885 755 484 444 1241 938 848 1321 429 1274 905 325
[13,] 275 199 200 94 62 106 174 173 104 264 98 184 179 80
[14,] 1469 877 924 791 606 512 1229 1045 1082 1344 435 1242 903 321
[15,] 1940 1396 1725 989 751 951 1406 1973 1585 2287 774 1710 1721 762
[16,] 1396 876 1107 764 643 705 1067 1339 1197 1535 601 1168 1043 418
[17,] 1725 1107 1126 948 690 631 1287 1288 1180 1651 555 1386 1102 445
[18,] 989 764 948 324 284 607 497 920 538 1210 501 599 793 446
[19,] 751 643 690 284 218 386 407 600 388 868 302 504 571 324
[20,] 951 705 631 607 386 324 802 637 686 879 267 913 605 236
[21,] 1406 1067 1287 497 407 802 736 1494 866 1856 636 897 1248 734
[22,] 1973 1339 1288 920 600 637 1494 1326 1105 1823 590 1612 1346 526
[23,] 1585 1197 1180 538 388 686 866 1105 624 1661 568 945 1054 628
[24,] 2287 1535 1651 1210 868 879 1856 1823 1661 2256 767 2059 1757 652
[25,] 774 601 555 501 302 267 636 590 568 767 232 774 544 214
[26,] 1710 1168 1386 599 504 913 897 1612 945 2059 774 990 1271 728
[27,] 1721 1043 1102 793 571 605 1248 1346 1054 1757 544 1271 1042 457
[28,] 762 418 445 446 324 236 734 526 628 652 214 728 457 122
[29,] 1626 1237 1371 663 539 784 1027 1252 919 1819 624 1145 1115 582
[30,] 1354 814 865 882 639 436 1292 981 1169 1198 371 1385 875 245
[1,] 827 477
[2,] 899 906
[3,] 716 582
[4,] 960 658
[5,] 1001 909
[6,] 924 983
[7,] 1469 1021
[8,] 948 1058
[9,] 1347 1372
[10,] 1092 1281
[11,] 829 878
[12,] 936 642
[13,] 141 166
[14,] 1154 659
[15,] 1626 1354
[16,] 1237 814
[17,] 1371 865
[18,] 663 882
[19,] 539 639
[20,] 784 436
[21,] 1027 1292
[22,] 1252 981
[23,] 919 1169
[24,] 1819 1198
[25,] 624 371
[26,] 1145 1385
[27,] 1115 875
[28,] 582 245
[29,] 1108 1119
[30,] 1119 466
Matrix^15
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 423062960022 5.458344e+11 385809257837 5.341710e+11 5.634876e+11
[2,] 545834416175 7.019260e+11 496578597519 6.889340e+11 7.250517e+11
[3,] 385809257837 4.965786e+11 351056567642 4.872370e+11 5.128841e+11
[4,] 534171047654 6.889340e+11 487237036534 6.741100e+11 7.112026e+11
[5,] 563487620303 7.250517e+11 512884139713 7.112026e+11 7.488732e+11
[6,] 493254652527 6.337131e+11 448396526133 6.225207e+11 6.547402e+11
[7,] 745373760712 9.602466e+11 678803660884 9.412428e+11 9.916002e+11
[8,] 563367163324 7.240342e+11 512343232328 7.109416e+11 7.479705e+11
[9,] 798332447356 1.026551e+12 726398794335 1.007388e+12 1.060357e+12
[10,] 598658088439 7.683683e+11 543684368860 7.556488e+11 7.940343e+11
[11,] 474840061047 6.101038e+11 431589928510 5.994399e+11 6.303408e+11
[12,] 535224143194 6.904095e+11 488338967155 6.753484e+11 7.126728e+11
[13,] 95846986188 1.232312e+11 87239758999 1.208958e+11 1.272814e+11
[14,] 556694181744 7.184287e+11 507886775113 7.027341e+11 7.416087e+11
[15,] 874795479971 1.125978e+12 796121647817 1.104603e+12 1.162947e+12
[16,] 601937090347 7.756910e+11 548327149099 7.600730e+11 8.009814e+11
[17,] 660857937532 8.520789e+11 602456357421 8.342169e+11 8.797249e+11
[18,] 409100882376 5.249052e+11 371495139778 5.163043e+11 5.424514e+11
[19,] 304691220792 3.912485e+11 276891722649 3.844939e+11 4.042668e+11
[20,] 374444157784 4.832748e+11 341666190993 4.726408e+11 4.988536e+11
[21,] 610951310379 7.840062e+11 554711993083 7.712711e+11 8.102193e+11
[22,] 722982845009 9.316168e+11 658989825572 9.123574e+11 9.618793e+11
[23,] 568575210787 7.301096e+11 516861158850 7.172943e+11 7.543485e+11
[24,] 932777530596 1.202506e+12 850213664489 1.177546e+12 1.241541e+12
[25,] 318483949066 4.108500e+11 290467067026 4.020429e+11 4.241305e+11
[26,] 676885363503 8.690257e+11 614917582900 8.543601e+11 8.979733e+11
[27,] 631701647201 8.138571e+11 575603297372 7.973051e+11 8.403577e+11
[28,] 287950244608 3.722133e+11 263055743771 3.635147e+11 3.840934e+11
[29,] 638165550242 8.205869e+11 580608427035 8.053333e+11 8.476497e+11
[30,] 540114383921 6.980789e+11 493306477962 6.819322e+11 7.203956e+11
[1,] 4.932547e+11 7.453738e+11 5.633672e+11 7.983324e+11 5.986581e+11
[2,] 6.337131e+11 9.602466e+11 7.240342e+11 1.026551e+12 7.683683e+11
[3,] 4.483965e+11 6.788037e+11 5.123432e+11 7.263988e+11 5.436844e+11
[4,] 6.225207e+11 9.412428e+11 7.109416e+11 1.007388e+12 7.556488e+11
[5,] 6.547402e+11 9.916002e+11 7.479705e+11 1.060357e+12 7.940343e+11
[6,] 5.720161e+11 8.673339e+11 6.535813e+11 9.267970e+11 6.933531e+11
[7,] 8.673339e+11 1.312106e+12 9.908633e+11 1.404585e+12 1.052051e+12
[8,] 6.535813e+11 9.908633e+11 7.467447e+11 1.058823e+12 7.923551e+11
[9,] 9.267970e+11 1.404585e+12 1.058823e+12 1.501124e+12 1.123819e+12
[10,] 6.933531e+11 1.052051e+12 7.923551e+11 1.123819e+12 8.400592e+11
[11,] 5.506741e+11 8.348721e+11 6.292614e+11 8.923670e+11 6.674164e+11
[12,] 6.238662e+11 9.432740e+11 7.124560e+11 1.009450e+12 7.573707e+11
[13,] 1.112518e+11 1.686697e+11 1.270909e+11 1.801606e+11 1.349223e+11
[14,] 6.492965e+11 9.810592e+11 7.415019e+11 1.050651e+12 7.882091e+11
[15,] 1.016786e+12 1.539299e+12 1.161712e+12 1.646978e+12 1.232967e+12
[16,] 7.007363e+11 1.059793e+12 8.004642e+11 1.134610e+12 8.500811e+11
[17,] 7.698690e+11 1.164072e+12 8.793093e+11 1.246130e+12 9.342766e+11
[18,] 4.736149e+11 7.188850e+11 5.412431e+11 7.676842e+11 5.738040e+11
[19,] 3.531091e+11 5.356639e+11 4.034734e+11 5.721667e+11 4.279523e+11
[20,] 4.367783e+11 6.599454e+11 4.987964e+11 7.067230e+11 5.302605e+11
[21,] 7.073882e+11 1.073479e+12 8.084672e+11 1.146769e+12 8.569605e+11
[22,] 8.415551e+11 1.273397e+12 9.612245e+11 1.362216e+12 1.021195e+12
[23,] 6.589296e+11 9.997708e+11 7.528702e+11 1.067568e+12 7.987132e+11
[24,] 1.086392e+12 1.642912e+12 1.240914e+12 1.758618e+12 1.318261e+12
[25,] 3.712489e+11 5.611544e+11 4.240148e+11 6.008368e+11 4.506054e+11
[26,] 7.842277e+11 1.189728e+12 8.961738e+11 1.271024e+12 9.502944e+11
[27,] 7.351626e+11 1.112379e+12 8.397345e+11 1.190185e+12 8.919823e+11
[28,] 3.365434e+11 5.078735e+11 3.842684e+11 5.443219e+11 4.087687e+11
[29,] 7.408876e+11 1.122723e+12 8.464145e+11 1.200014e+12 8.983599e+11
[30,] 6.311511e+11 9.524998e+11 7.206931e+11 1.020921e+12 7.665186e+11
[1,] 4.748401e+11 5.352241e+11 95846986188 5.566942e+11 8.747955e+11
[2,] 6.101038e+11 6.904095e+11 123231173606 7.184287e+11 1.125978e+12
[3,] 4.315899e+11 4.883390e+11 87239758999 5.078868e+11 7.961216e+11
[4,] 5.994399e+11 6.753484e+11 120895774634 7.027341e+11 1.104603e+12
[5,] 6.303408e+11 7.126728e+11 127281395705 7.416087e+11 1.162947e+12
[6,] 5.506741e+11 6.238662e+11 111251809964 6.492965e+11 1.016786e+12
[7,] 8.348721e+11 9.432740e+11 168669723831 9.810592e+11 1.539299e+12
[8,] 6.292614e+11 7.124560e+11 127090888012 7.415019e+11 1.161712e+12
[9,] 8.923670e+11 1.009450e+12 180160615750 1.050651e+12 1.646978e+12
[10,] 6.674164e+11 7.573707e+11 134922313677 7.882091e+11 1.232967e+12
[11,] 5.300826e+11 6.007970e+11 107144619737 6.251264e+11 9.787247e+11
[12,] 6.007970e+11 6.765425e+11 121126296838 7.040500e+11 1.107017e+12
[13,] 1.071446e+11 1.211263e+11 21614107182 1.261149e+11 1.977678e+11
[14,] 6.251264e+11 7.040500e+11 126114905791 7.324158e+11 1.151525e+12
[15,] 9.787247e+11 1.107017e+12 197767792300 1.151525e+12 1.805360e+12
[16,] 6.745129e+11 7.616770e+11 136240661830 7.922186e+11 1.243421e+12
[17,] 7.411924e+11 8.358438e+11 149586985199 8.695614e+11 1.365988e+12
[18,] 4.559353e+11 5.174799e+11 92156822862 5.386093e+11 8.424387e+11
[19,] 3.399478e+11 3.853200e+11 68675139530 4.010884e+11 6.278670e+11
[20,] 4.205364e+11 4.735027e+11 84824252560 4.926186e+11 7.746226e+11
[21,] 6.808991e+11 7.730967e+11 137699024027 8.044593e+11 1.258013e+12
[22,] 8.103616e+11 9.140735e+11 163476789955 9.512315e+11 1.493980e+12
[23,] 6.344816e+11 7.187783e+11 128107555775 7.483360e+11 1.171882e+12
[24,] 1.045922e+12 1.179864e+12 211112724146 1.227424e+12 1.927730e+12
[25,] 3.574326e+11 4.028079e+11 72122916183 4.190434e+11 6.585589e+11
[26,] 7.549351e+11 8.563133e+11 152596290311 8.911306e+11 1.394465e+12
[27,] 7.078273e+11 7.988927e+11 142861844710 8.312221e+11 1.305061e+12
[28,] 3.240333e+11 3.641573e+11 65336055364 3.787664e+11 5.963808e+11
[29,] 7.133069e+11 8.069947e+11 144029330178 8.399111e+11 1.316488e+12
[30,] 6.076464e+11 6.831636e+11 122554875330 7.105231e+11 1.118434e+12
[1,] 6.019371e+11 6.608579e+11 409100882376 304691220792 374444157784
[2,] 7.756910e+11 8.520789e+11 524905206057 391248514597 483274814626
[3,] 5.483271e+11 6.024564e+11 371495139778 276891722649 341666190993
[4,] 7.600730e+11 8.342169e+11 516304297004 384493927296 472640775080
[5,] 8.009814e+11 8.797249e+11 542451392030 404266774644 498853559145
[6,] 7.007363e+11 7.698690e+11 473614907014 353109099172 436778283459
[7,] 1.059793e+12 1.164072e+12 718885049941 535663918064 659945418858
[8,] 8.004642e+11 8.793093e+11 541243067039 403473382293 498796376533
[9,] 1.134610e+12 1.246130e+12 767684154669 572166651741 706723006900
[10,] 8.500811e+11 9.342766e+11 573804032190 427952334326 530260489802
[11,] 6.745129e+11 7.411924e+11 455935299443 339947818896 420536439337
[12,] 7.616770e+11 8.358438e+11 517479876225 385320006130 473502727883
[13,] 1.362407e+11 1.495870e+11 92156822862 68675139530 84824252560
[14,] 7.922186e+11 8.695614e+11 538609276587 401088413135 492618636840
[15,] 1.243421e+12 1.365988e+12 842438715842 627867040773 774622575947
[16,] 8.559676e+11 9.401037e+11 580868810368 432793918574 532916076257
[17,] 9.401037e+11 1.032104e+12 638388309697 475507354579 584883398856
[18,] 5.808688e+11 6.383883e+11 391912019008 292305802761 362347995901
[19,] 4.327939e+11 4.755074e+11 292305802761 217953147926 269807898661
[20,] 5.329161e+11 5.848834e+11 362347995901 269807898661 331317321914
[21,] 8.674089e+11 9.534627e+11 585362268969 436612216449 541211216465
[22,] 1.028393e+12 1.128908e+12 697708425015 519694132957 639776148044
[23,] 8.077172e+11 8.872385e+11 545515717888 406702014538 503374239063
[24,] 1.326829e+12 1.456780e+12 900777573579 670976648266 825582897088
[25,] 4.531654e+11 4.974468e+11 307917133023 229312406927 281840715377
[26,] 9.612584e+11 1.056379e+12 649106117765 484068676919 599505840286
[27,] 8.983919e+11 9.864031e+11 609429496256 454009455973 559104738056
[28,] 4.100347e+11 4.499083e+11 279362261641 207941348670 254741092457
[29,] 9.069567e+11 9.961652e+11 613668697594 457402395715 564978416061
[30,] 7.690429e+11 8.439211e+11 523871658567 389968586301 477870094037
[1,] 6.109513e+11 7.229828e+11 5.685752e+11 9.327775e+11 318483949066
[2,] 7.840062e+11 9.316168e+11 7.301096e+11 1.202506e+12 410849976213
[3,] 5.547120e+11 6.589898e+11 5.168612e+11 8.502137e+11 290467067026
[4,] 7.712711e+11 9.123574e+11 7.172943e+11 1.177546e+12 402042934440
[5,] 8.102193e+11 9.618793e+11 7.543485e+11 1.241541e+12 424130523269
[6,] 7.073882e+11 8.415551e+11 6.589296e+11 1.086392e+12 371248872366
[7,] 1.073479e+12 1.273397e+12 9.997708e+11 1.642912e+12 561154390753
[8,] 8.084672e+11 9.612245e+11 7.528702e+11 1.240914e+12 424014797853
[9,] 1.146769e+12 1.362216e+12 1.067568e+12 1.758618e+12 600836796304
[10,] 8.569605e+11 1.021195e+12 7.987132e+11 1.318261e+12 450605421293
[11,] 6.808991e+11 8.103616e+11 6.344816e+11 1.045922e+12 357432565730
[12,] 7.730967e+11 9.140735e+11 7.187783e+11 1.179864e+12 402807939715
[13,] 1.376990e+11 1.634768e+11 1.281076e+11 2.111127e+11 72122916183
[14,] 8.044593e+11 9.512315e+11 7.483360e+11 1.227424e+12 419043369524
[15,] 1.258013e+12 1.493980e+12 1.171882e+12 1.927730e+12 658558924779
[16,] 8.674089e+11 1.028393e+12 8.077172e+11 1.326829e+12 453165367497
[17,] 9.534627e+11 1.128908e+12 8.872385e+11 1.456780e+12 497446833568
[18,] 5.853623e+11 6.977084e+11 5.455157e+11 9.007776e+11 307917133023
[19,] 4.366122e+11 5.196941e+11 4.067020e+11 6.709766e+11 229312406927
[20,] 5.412112e+11 6.397761e+11 5.033742e+11 8.255829e+11 281840715377
[21,] 8.741698e+11 1.042272e+12 8.149674e+11 1.345349e+12 459891360476
[22,] 1.042272e+12 1.234439e+12 9.695701e+11 1.593393e+12 544130078021
[23,] 8.149674e+11 9.695701e+11 7.587940e+11 1.252040e+12 427867967793
[24,] 1.345349e+12 1.593393e+12 1.252040e+12 2.056120e+12 702138077425
[25,] 4.598914e+11 5.441301e+11 4.278680e+11 7.021381e+11 239728896736
[26,] 9.694565e+11 1.154766e+12 9.034236e+11 1.490666e+12 509498764624
[27,] 9.102894e+11 1.078764e+12 8.471153e+11 1.392270e+12 475482704370
[28,] 4.172588e+11 4.922942e+11 3.879474e+11 6.351342e+11 216759203174
[29,] 9.166489e+11 1.088981e+12 8.534546e+11 1.405815e+12 480306232907
[30,] 7.824017e+11 9.234492e+11 7.276020e+11 1.191313e+12 406592325661
[1,] 6.768854e+11 6.317016e+11 287950244608 6.381656e+11 5.401144e+11
[2,] 8.690257e+11 8.138571e+11 372213264478 8.205869e+11 6.980789e+11
[3,] 6.149176e+11 5.756033e+11 263055743771 5.806084e+11 4.933065e+11
[4,] 8.543601e+11 7.973051e+11 363514720305 8.053333e+11 6.819322e+11
[5,] 8.979733e+11 8.403577e+11 384093433305 8.476497e+11 7.203956e+11
[6,] 7.842277e+11 7.351626e+11 336543432448 7.408876e+11 6.311511e+11
[7,] 1.189728e+12 1.112379e+12 507873513216 1.122723e+12 9.524998e+11
[8,] 8.961738e+11 8.397345e+11 384268351998 8.464145e+11 7.206931e+11
[9,] 1.271024e+12 1.190185e+12 544321910161 1.200014e+12 1.020921e+12
[10,] 9.502944e+11 8.919823e+11 408768662772 8.983599e+11 7.665186e+11
[11,] 7.549351e+11 7.078273e+11 324033267496 7.133069e+11 6.076464e+11
[12,] 8.563133e+11 7.988927e+11 364157294075 8.069947e+11 6.831636e+11
[13,] 1.525963e+11 1.428618e+11 65336055364 1.440293e+11 1.225549e+11
[14,] 8.911306e+11 8.312221e+11 378766423376 8.399111e+11 7.105231e+11
[15,] 1.394465e+12 1.305061e+12 596380767435 1.316488e+12 1.118434e+12
[16,] 9.612584e+11 8.983919e+11 410034735336 9.069567e+11 7.690429e+11
[17,] 1.056379e+12 9.864031e+11 449908320328 9.961652e+11 8.439211e+11
[18,] 6.491061e+11 6.094295e+11 279362261641 6.136687e+11 5.238717e+11
[19,] 4.840687e+11 4.540095e+11 207941348670 4.574024e+11 3.899686e+11
[20,] 5.995058e+11 5.591047e+11 254741092457 5.649784e+11 4.778701e+11
[21,] 9.694565e+11 9.102894e+11 417258818870 9.166489e+11 7.824017e+11
[22,] 1.154766e+12 1.078764e+12 492294179721 1.088981e+12 9.234492e+11
[23,] 9.034236e+11 8.471153e+11 387947369237 8.534546e+11 7.276020e+11
[24,] 1.490666e+12 1.392270e+12 635134161478 1.405815e+12 1.191313e+12
[25,] 5.094988e+11 4.754827e+11 216759203174 4.803062e+11 4.065923e+11
[26,] 1.074935e+12 1.008621e+12 462078408154 1.016003e+12 8.665211e+11
[27,] 1.008621e+12 9.425478e+11 430235341792 9.514178e+11 8.070080e+11
[28,] 4.620784e+11 4.302353e+11 195716866016 4.351383e+11 3.671779e+11
[29,] 1.016003e+12 9.514178e+11 435138316764 9.593138e+11 8.161280e+11
[30,] 8.665211e+11 8.070080e+11 367177895240 8.161280e+11 6.888170e+11
Matrix^30
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 9.966249e+24 1.282927e+25 9.073809e+24 1.257998e+25 1.324958e+25
[2,] 1.282927e+25 1.651482e+25 1.168049e+25 1.619385e+25 1.705586e+25
[3,] 9.073809e+24 1.168049e+25 8.261303e+24 1.145349e+25 1.206316e+25
[4,] 1.257998e+25 1.619385e+25 1.145349e+25 1.587917e+25 1.672439e+25
[5,] 1.324958e+25 1.705586e+25 1.206316e+25 1.672439e+25 1.761463e+25
[6,] 1.158603e+25 1.491444e+25 1.054858e+25 1.462456e+25 1.540305e+25
[7,] 1.754122e+25 2.258036e+25 1.597049e+25 2.214155e+25 2.332012e+25
[8,] 1.323575e+25 1.703808e+25 1.205058e+25 1.670693e+25 1.759626e+25
[9,] 1.876252e+25 2.415255e+25 1.708246e+25 2.368314e+25 2.494381e+25
[10,] 1.405243e+25 1.808940e+25 1.279415e+25 1.773779e+25 1.868202e+25
[11,] 1.115424e+25 1.435861e+25 1.015546e+25 1.407953e+25 1.482901e+25
[12,] 1.260594e+25 1.622727e+25 1.147712e+25 1.591194e+25 1.675890e+25
[13,] 2.252318e+24 2.899356e+24 2.050637e+24 2.843007e+24 2.994342e+24
[14,] 1.311631e+25 1.688425e+25 1.194179e+25 1.655617e+25 1.743741e+25
[15,] 2.057441e+25 2.648493e+25 1.873209e+25 2.597021e+25 2.735260e+25
[16,] 1.416861e+25 1.823888e+25 1.289988e+25 1.788444e+25 1.883641e+25
[17,] 1.556075e+25 2.003093e+25 1.416735e+25 1.964168e+25 2.068717e+25
[18,] 9.600706e+24 1.235879e+25 8.741042e+24 1.211857e+25 1.276367e+25
[19,] 7.154230e+24 9.209487e+24 6.513623e+24 9.030485e+24 9.511195e+24
[20,] 8.822766e+24 1.135729e+25 8.032716e+24 1.113661e+25 1.172938e+25
[21,] 1.433937e+25 1.845878e+25 1.305539e+25 1.809998e+25 1.906349e+25
[22,] 1.701588e+25 2.190408e+25 1.549218e+25 2.147842e+25 2.262169e+25
[23,] 1.335006e+25 1.718524e+25 1.215466e+25 1.685122e+25 1.774824e+25
[24,] 2.196115e+25 2.827000e+25 1.999462e+25 2.772064e+25 2.919616e+25
[25,] 7.501711e+24 9.656742e+24 6.829961e+24 9.469094e+24 9.973112e+24
[26,] 1.589182e+25 2.045720e+25 1.446883e+25 2.005957e+25 2.112739e+25
[27,] 1.486630e+25 1.913700e+25 1.353509e+25 1.876510e+25 1.976395e+25
[28,] 6.791980e+24 8.743105e+24 6.183772e+24 8.573229e+24 9.029547e+24
[29,] 1.499848e+25 1.930719e+25 1.365546e+25 1.893195e+25 1.993971e+25
[30,] 1.273884e+25 1.639831e+25 1.159810e+25 1.607970e+25 1.693555e+25
[1,] 1.158603e+25 1.754122e+25 1.323575e+25 1.876252e+25 1.405243e+25
[2,] 1.491444e+25 2.258036e+25 1.703808e+25 2.415255e+25 1.808940e+25
[3,] 1.054858e+25 1.597049e+25 1.205058e+25 1.708246e+25 1.279415e+25
[4,] 1.462456e+25 2.214155e+25 1.670693e+25 2.368314e+25 1.773779e+25
[5,] 1.540305e+25 2.332012e+25 1.759626e+25 2.494381e+25 1.868202e+25
[6,] 1.346915e+25 2.039218e+25 1.538699e+25 2.181203e+25 1.633645e+25
[7,] 2.039218e+25 3.087368e+25 2.329580e+25 3.302327e+25 2.473323e+25
[8,] 1.538699e+25 2.329580e+25 1.757792e+25 2.491781e+25 1.866256e+25
[9,] 2.181203e+25 3.302327e+25 2.491781e+25 3.532256e+25 2.645534e+25
[10,] 1.633645e+25 2.473323e+25 1.866256e+25 2.645534e+25 1.981414e+25
[11,] 1.296718e+25 1.963221e+25 1.481355e+25 2.099914e+25 1.572762e+25
[12,] 1.465474e+25 2.218723e+25 1.674140e+25 2.373201e+25 1.777439e+25
[13,] 2.618392e+24 3.964228e+24 2.991220e+24 4.240243e+24 3.175791e+24
[14,] 1.524805e+25 2.308552e+25 1.741920e+25 2.469284e+25 1.849401e+25
[15,] 2.391838e+25 3.621230e+25 2.732408e+25 3.873361e+25 2.901009e+25
[16,] 1.647142e+25 2.493766e+25 1.881676e+25 2.667395e+25 1.997781e+25
[17,] 1.808980e+25 2.738790e+25 2.066558e+25 2.929478e+25 2.194071e+25
[18,] 1.116116e+25 1.689789e+25 1.275038e+25 1.807446e+25 1.353715e+25
[19,] 8.317038e+24 1.259193e+25 9.501285e+24 1.346867e+25 1.008756e+25
[20,] 1.025669e+25 1.552862e+25 1.171713e+25 1.660978e+25 1.244011e+25
[21,] 1.667003e+25 2.523826e+25 1.904363e+25 2.699554e+25 2.021873e+25
[22,] 1.978144e+25 2.994902e+25 2.259809e+25 3.203423e+25 2.399246e+25
[23,] 1.551990e+25 2.349700e+25 1.772975e+25 2.513303e+25 1.882376e+25
[24,] 2.553045e+25 3.865302e+25 2.916569e+25 4.134423e+25 3.096531e+25
[25,] 8.720940e+24 1.320348e+25 9.962703e+24 1.412277e+25 1.057743e+25
[26,] 1.847479e+25 2.797067e+25 2.110538e+25 2.991819e+25 2.240769e+25
[27,] 1.728250e+25 2.616563e+25 1.974333e+25 2.798742e+25 2.096156e+25
[28,] 7.895835e+24 1.195430e+25 9.020114e+24 1.278659e+25 9.576669e+24
[29,] 1.743621e+25 2.639831e+25 1.991892e+25 2.823633e+25 2.114801e+25
[30,] 1.480920e+25 2.242113e+25 1.691787e+25 2.398217e+25 1.796173e+25
[1,] 1.115424e+25 1.260594e+25 2.252318e+24 1.311631e+25 2.057441e+25
[2,] 1.435861e+25 1.622727e+25 2.899356e+24 1.688425e+25 2.648493e+25
[3,] 1.015546e+25 1.147712e+25 2.050637e+24 1.194179e+25 1.873209e+25
[4,] 1.407953e+25 1.591194e+25 2.843007e+24 1.655617e+25 2.597021e+25
[5,] 1.482901e+25 1.675890e+25 2.994342e+24 1.743741e+25 2.735260e+25
[6,] 1.296718e+25 1.465474e+25 2.618392e+24 1.524805e+25 2.391838e+25
[7,] 1.963221e+25 2.218723e+25 3.964228e+24 2.308552e+25 3.621230e+25
[8,] 1.481355e+25 1.674140e+25 2.991220e+24 1.741920e+25 2.732408e+25
[9,] 2.099914e+25 2.373201e+25 4.240243e+24 2.469284e+25 3.873361e+25
[10,] 1.572762e+25 1.777439e+25 3.175791e+24 1.849401e+25 2.901009e+25
[11,] 1.248392e+25 1.410858e+25 2.520810e+24 1.467979e+25 2.302699e+25
[12,] 1.410858e+25 1.594478e+25 2.848874e+24 1.659033e+25 2.602380e+25
[13,] 2.520810e+24 2.848874e+24 5.090136e+23 2.964214e+24 4.649717e+24
[14,] 1.467979e+25 1.659033e+25 2.964214e+24 1.726202e+25 2.707741e+25
[15,] 2.302699e+25 2.602380e+25 4.649717e+24 2.707741e+25 4.247407e+25
[16,] 1.585756e+25 1.792134e+25 3.202033e+24 1.864692e+25 2.924983e+25
[17,] 1.741563e+25 1.968221e+25 3.516648e+24 2.047908e+25 3.212376e+25
[18,] 1.074521e+25 1.214357e+25 2.169720e+24 1.263522e+25 1.981987e+25
[19,] 8.007080e+24 9.049118e+24 1.616826e+24 9.415484e+24 1.476931e+25
[20,] 9.874447e+24 1.115959e+25 1.993896e+24 1.161141e+25 1.821378e+25
[21,] 1.604877e+25 1.813732e+25 3.240638e+24 1.887164e+25 2.960245e+25
[22,] 1.904422e+25 2.152275e+25 3.845501e+24 2.239413e+25 3.512775e+25
[23,] 1.494151e+25 1.688599e+25 3.017056e+24 1.756964e+25 2.756008e+25
[24,] 2.457898e+25 2.777784e+25 4.963106e+24 2.890248e+25 4.533681e+25
[25,] 8.395928e+24 9.488634e+24 1.695346e+24 9.872799e+24 1.548660e+25
[26,] 1.778627e+25 2.010096e+25 3.591484e+24 2.091478e+25 3.280734e+25
[27,] 1.663842e+25 1.880383e+25 3.359708e+24 1.956513e+25 3.069014e+25
[28,] 7.601572e+24 8.590923e+24 1.534947e+24 8.938744e+24 1.402139e+25
[29,] 1.678640e+25 1.897101e+25 3.389587e+24 1.973909e+25 3.096307e+25
[30,] 1.425729e+25 1.611288e+25 2.878903e+24 1.676524e+25 2.629812e+25
[1,] 1.416861e+25 1.556075e+25 9.600706e+24 7.154230e+24 8.822766e+24
[2,] 1.823888e+25 2.003093e+25 1.235879e+25 9.209487e+24 1.135729e+25
[3,] 1.289988e+25 1.416735e+25 8.741042e+24 6.513623e+24 8.032716e+24
[4,] 1.788444e+25 1.964168e+25 1.211857e+25 9.030485e+24 1.113661e+25
[5,] 1.883641e+25 2.068717e+25 1.276367e+25 9.511195e+24 1.172938e+25
[6,] 1.647142e+25 1.808980e+25 1.116116e+25 8.317038e+24 1.025669e+25
[7,] 2.493766e+25 2.738790e+25 1.689789e+25 1.259193e+25 1.552862e+25
[8,] 1.881676e+25 2.066558e+25 1.275038e+25 9.501285e+24 1.171713e+25
[9,] 2.667395e+25 2.929478e+25 1.807446e+25 1.346867e+25 1.660978e+25
[10,] 1.997781e+25 2.194071e+25 1.353715e+25 1.008756e+25 1.244011e+25
[11,] 1.585756e+25 1.741563e+25 1.074521e+25 8.007080e+24 9.874447e+24
[12,] 1.792134e+25 1.968221e+25 1.214357e+25 9.049118e+24 1.115959e+25
[13,] 3.202033e+24 3.516648e+24 2.169720e+24 1.616826e+24 1.993896e+24
[14,] 1.864692e+25 2.047908e+25 1.263522e+25 9.415484e+24 1.161141e+25
[15,] 2.924983e+25 3.212376e+25 1.981987e+25 1.476931e+25 1.821378e+25
[16,] 2.014295e+25 2.212209e+25 1.364896e+25 1.017090e+25 1.254296e+25
[17,] 2.212209e+25 2.429570e+25 1.499003e+25 1.117023e+25 1.377538e+25
[18,] 1.364896e+25 1.499003e+25 9.248666e+24 6.891887e+24 8.499155e+24
[19,] 1.017090e+25 1.117023e+25 6.891887e+24 5.135672e+24 6.333381e+24
[20,] 1.254296e+25 1.377538e+25 8.499155e+24 6.333381e+24 7.810482e+24
[21,] 2.038574e+25 2.238872e+25 1.381357e+25 1.029354e+25 1.269412e+25
[22,] 2.419079e+25 2.656765e+25 1.639180e+25 1.221480e+25 1.506355e+25
[23,] 1.897927e+25 2.084406e+25 1.286051e+25 9.583353e+24 1.181832e+25
[24,] 3.122128e+25 3.428893e+25 2.115569e+25 1.576474e+25 1.944142e+25
[25,] 1.066488e+25 1.171276e+25 7.226563e+24 5.385072e+24 6.640998e+24
[26,] 2.259280e+25 2.481263e+25 1.530908e+25 1.140796e+25 1.406845e+25
[27,] 2.113482e+25 2.321142e+25 1.432107e+25 1.067173e+25 1.316060e+25
[28,] 9.655872e+24 1.060462e+25 6.542837e+24 4.875579e+24 6.012701e+24
[29,] 2.132275e+25 2.341781e+25 1.444845e+25 1.076665e+25 1.327761e+25
[30,] 1.811027e+25 1.988971e+25 1.227156e+25 9.144495e+24 1.127724e+25
[1,] 1.433937e+25 1.701588e+25 1.335006e+25 2.196115e+25 7.501711e+24
[2,] 1.845878e+25 2.190408e+25 1.718524e+25 2.827000e+25 9.656742e+24
[3,] 1.305539e+25 1.549218e+25 1.215466e+25 1.999462e+25 6.829961e+24
[4,] 1.809998e+25 2.147842e+25 1.685122e+25 2.772064e+25 9.469094e+24
[5,] 1.906349e+25 2.262169e+25 1.774824e+25 2.919616e+25 9.973112e+24
[6,] 1.667003e+25 1.978144e+25 1.551990e+25 2.553045e+25 8.720940e+24
[7,] 2.523826e+25 2.994902e+25 2.349700e+25 3.865302e+25 1.320348e+25
[8,] 1.904363e+25 2.259809e+25 1.772975e+25 2.916569e+25 9.962703e+24
[9,] 2.699554e+25 3.203423e+25 2.513303e+25 4.134423e+25 1.412277e+25
[10,] 2.021873e+25 2.399246e+25 1.882376e+25 3.096531e+25 1.057743e+25
[11,] 1.604877e+25 1.904422e+25 1.494151e+25 2.457898e+25 8.395928e+24
[12,] 1.813732e+25 2.152275e+25 1.688599e+25 2.777784e+25 9.488634e+24
[13,] 3.240638e+24 3.845501e+24 3.017056e+24 4.963106e+24 1.695346e+24
[14,] 1.887164e+25 2.239413e+25 1.756964e+25 2.890248e+25 9.872799e+24
[15,] 2.960245e+25 3.512775e+25 2.756008e+25 4.533681e+25 1.548660e+25
[16,] 2.038574e+25 2.419079e+25 1.897927e+25 3.122128e+25 1.066488e+25
[17,] 2.238872e+25 2.656765e+25 2.084406e+25 3.428893e+25 1.171276e+25
[18,] 1.381357e+25 1.639180e+25 1.286051e+25 2.115569e+25 7.226563e+24
[19,] 1.029354e+25 1.221480e+25 9.583353e+24 1.576474e+25 5.385072e+24
[20,] 1.269412e+25 1.506355e+25 1.181832e+25 1.944142e+25 6.640998e+24
[21,] 2.063159e+25 2.448236e+25 1.920813e+25 3.159759e+25 1.079341e+25
[22,] 2.448236e+25 2.905207e+25 2.279326e+25 3.749538e+25 1.280805e+25
[23,] 1.920813e+25 2.279326e+25 1.788289e+25 2.941759e+25 1.004875e+25
[24,] 3.159759e+25 3.749538e+25 2.941759e+25 4.839255e+25 1.653041e+25
[25,] 1.079341e+25 1.280805e+25 1.004875e+25 1.653041e+25 5.646625e+24
[26,] 2.286524e+25 2.713294e+25 2.128768e+25 3.501849e+25 1.196195e+25
[27,] 2.138957e+25 2.538199e+25 1.991385e+25 3.275868e+25 1.119003e+25
[28,] 9.772213e+24 1.159628e+25 9.098012e+24 1.496647e+25 5.112401e+24
[29,] 2.157983e+25 2.560768e+25 2.009097e+25 3.304996e+25 1.128953e+25
[30,] 1.832848e+25 2.174964e+25 1.706397e+25 2.807068e+25 9.588670e+24
[1,] 1.589182e+25 1.486630e+25 6.791980e+24 1.499848e+25 1.273884e+25
[2,] 2.045720e+25 1.913700e+25 8.743105e+24 1.930719e+25 1.639831e+25
[3,] 1.446883e+25 1.353509e+25 6.183772e+24 1.365546e+25 1.159810e+25
[4,] 2.005957e+25 1.876510e+25 8.573229e+24 1.893195e+25 1.607970e+25
[5,] 2.112739e+25 1.976395e+25 9.029547e+24 1.993971e+25 1.693555e+25
[6,] 1.847479e+25 1.728250e+25 7.895835e+24 1.743621e+25 1.480920e+25
[7,] 2.797067e+25 2.616563e+25 1.195430e+25 2.639831e+25 2.242113e+25
[8,] 2.110538e+25 1.974333e+25 9.020114e+24 1.991892e+25 1.691787e+25
[9,] 2.991819e+25 2.798742e+25 1.278659e+25 2.823633e+25 2.398217e+25
[10,] 2.240769e+25 2.096156e+25 9.576669e+24 2.114801e+25 1.796173e+25
[11,] 1.778627e+25 1.663842e+25 7.601572e+24 1.678640e+25 1.425729e+25
[12,] 2.010096e+25 1.880383e+25 8.590923e+24 1.897101e+25 1.611288e+25
[13,] 3.591484e+24 3.359708e+24 1.534947e+24 3.389587e+24 2.878903e+24
[14,] 2.091478e+25 1.956513e+25 8.938744e+24 1.973909e+25 1.676524e+25
[15,] 3.280734e+25 3.069014e+25 1.402139e+25 3.096307e+25 2.629812e+25
[16,] 2.259280e+25 2.113482e+25 9.655872e+24 2.132275e+25 1.811027e+25
[17,] 2.481263e+25 2.321142e+25 1.060462e+25 2.341781e+25 1.988971e+25
[18,] 1.530908e+25 1.432107e+25 6.542837e+24 1.444845e+25 1.227156e+25
[19,] 1.140796e+25 1.067173e+25 4.875579e+24 1.076665e+25 9.144495e+24
[20,] 1.406845e+25 1.316060e+25 6.012701e+24 1.327761e+25 1.127724e+25
[21,] 2.286524e+25 2.138957e+25 9.772213e+24 2.157983e+25 1.832848e+25
[22,] 2.713294e+25 2.538199e+25 1.159628e+25 2.560768e+25 2.174964e+25
[23,] 2.128768e+25 1.991385e+25 9.098012e+24 2.009097e+25 1.706397e+25
[24,] 3.501849e+25 3.275868e+25 1.496647e+25 3.304996e+25 2.807068e+25
[25,] 1.196195e+25 1.119003e+25 5.112401e+24 1.128953e+25 9.588670e+24
[26,] 2.534072e+25 2.370531e+25 1.083021e+25 2.391616e+25 2.031282e+25
[27,] 2.370531e+25 2.217554e+25 1.013134e+25 2.237273e+25 1.900205e+25
[28,] 1.083021e+25 1.013134e+25 4.628728e+24 1.022141e+25 8.681504e+24
[29,] 2.391616e+25 2.237273e+25 1.022141e+25 2.257170e+25 1.917098e+25
[30,] 2.031282e+25 1.900205e+25 8.681504e+24 1.917098e+25 1.628277e+25